On uniform global asymptotic stability of adaptive systems with unknown control gains

We study adaptive tracking control problems for nonlinear systems in feedback form with multiple inputs and unknown high-frequency control gains. We design controllers that yield uniform global asymptotic stability for the error dynamics, which implies parameter estimation and tracking for the original systems. Our proof relies on a new global strict Lyapunov function construction. We apply our result to a brushless DC motor turning a mechanical load. We use integral input-to-state stability to quantify the effects of time-varying uncertainties on the motor electric parameters.